Trevor Gunn (he/they)

About me

I am a sixth year PhD student at Georgia Tech. I am interested in algebraic combinatorics and combinatorial algebraic geometry. Right now I am studying how to factor polynomials over hyperfields with an aim of developing a theory of intersection multiplicities. Previous to that, I studied divisor theory on abstract tropical curves with application to faithful tropicalization.

My advisor is Matt Baker.

I received my BMath from the University of Waterloo with majors in Pure Mathematics and Combinatorics & Optimization.

My curriculum vitæ

High School Math Day – April 22

Together with Wade Bloomquist and Evelyne Smith-Roberge, we are reshaping the old High School Math Competition to appeal to a broader audience. The new event will feature:

• Board games and other fun investigative math activities (e.g. soap films)
• A new logic based competition track focusing on more puzzle based math rather than algebra or geometry
• Prizes for new competitors and creative solutions to open ended problems

Registration and info at https://hsmd.math.gatech.edu/. Also see our promotional flier.

Seminars and miscellaneous

• Algebraic Student Seminar:

  https://sites.google.com/view/ga-sas

  I organize the Algebra Student Seminar at Georgia Tech together with Kevin Shu. Previously with Cvetelina Hill, Marc Härkönen and Jaewoo Jung The seminar is intended for graduate students to talk about their research or present on topics they are interested in learning about.

• Graduate Student Colloquium:

  I organize the Graduate Student Colloquium together with Abhishek Dhawan and Roberta Shapiro.

  Currently the colloquia meet before other School of Math social events such as board game nights.

  The colloquium is looking for speakers! Please reach out to one of us if you are interested in giving a talk.

• Some miscellaneous expository notes (work halted)

  I have some notes on some various topics in combinatorics and tropical geometry. This project is on pause while I complete my thesis.

• Lorentzian Polynomial Learning Seminar

  Some resources for a learning seminar I helped organize in 2019 on Lorentzian Polynomials

Research

• November, 2022 – Tropical Extensions and Baker-Lorscheid Multiplicities for Idylls 2211.06480 [Math.RA] (slides)
• December, 2019 – with Philipp Jell – Construction of Fully Faithful Tropicalizations for Curves in Ambient Dimension 3 1912.02648 [Math.AG]
• November, 2019 – A Newton Polygon Rule for Formally-Real Valued Fields and Multiplicities over the Signed Tropical Hyperfield 1911.12274 [Math.RA]

Resources

Tropical Geometry

For a quick explanation of tropical geometry, Madeline Brandt has an 8 minute video explanation on YouTube. For a longer, but still quite approachable, introduction to tropical geometry, I recommend this survey article by Ralph Morrison. For higher level general treatments of the subject, here are some books:

• Introduction to Tropical Geometry by Diane Maclagan and Bernd Sturmfels
• Essentials of Tropical Combinatorics by Michael Joswig

Hyperfields

For learning about hyperfields and multiplicities for polynomials over hyperfields, the original article Descartes' rule of signs, Newton polygons, and polynomials over hyperfields by my advisor, Matt Baker, and Oliver Lorscheid should be accessible to anyone with some familiarity with abstract algebra and mathematical maturity.

Ordered Blueprints

Oliver Lorscheid naturally has several papers describing ordered blueprints. For a starting point, I recommend looking at his lecture notes. I strongly suggest having good familiarity with commutative algebra and some category theory for these.